It depends on the comfort-with-code level of the designer, but these days, I do believe every designer is working with code in the actual Basecamp code base. (On its own separate branch with Git, of course.)

HTML is the shared language between designer and programmer, so more often than not these HTML designs are in local copies of Basecamp running on all of our machines.

Designer: “Hey, I made a design update to the form when you enter to-dos.” Programmer: “Awesome! I’ll pull down your branch, review, hook it up, and pass it back.” Designer: “Thank you! Let‘s celebrate with pizza.”